Overview

Questions

  1. How does synchrony of tree growth vary across regional/elevation gradients? Prediction: higher synchrony in lower latitude and lower elevation (drier) populations (SIASH, dendrochronological principles)

  2. Within populations is intraspecific synchrony greater than interspecific synchrony? Between specific species pairs? With increasing distance? Prediction: higher synchrony among intraspecific pairs, potentially higher synchrony between pine pairs versus pine-fir pairs (successional stages), and lower synchrony with increasing distance

  3. How has synchrony changed through time? Are changes more dramatic in certain populations? Is increased or decreased synchrony associated with certain environmental variables? Prediction: synchrony has increased with time, increased synchrony associated with drier, more variable time windows, changes are more pronounced in xeric populations.

Synchrony is explored here through residual correlations betweeen trees from multivariate models of tree growth.

Q2 Intra-interspecific competition

Pairwise pearson correlation summaires:

We calculated the correlation between series of tree ring growth for all unique pairs of individuals within competitive neighborhoods.

## # A tibble: 10 x 6
## # Groups:   spp1, spp2 [10]
##    spp1  spp2  pair    med  mean    sd
##    <chr> <chr> <chr> <dbl> <dbl> <dbl>
##  1 ac    ac    ac-ac 0.442 0.442 0.227
##  2 ac    pj    ac-pj 0.301 0.287 0.225
##  3 ac    pl    ac-pl 0.298 0.292 0.217
##  4 ac    pp    ac-pp 0.125 0.132 0.191
##  5 pj    pj    pj-pj 0.281 0.288 0.210
##  6 pj    pl    pj-pl 0.206 0.236 0.222
##  7 pj    pp    pj-pp 0.555 0.486 0.215
##  8 pl    pl    pl-pl 0.516 0.459 0.263
##  9 pl    pp    pl-pp 0.347 0.330 0.223
## 10 pp    pp    pp-pp 0.357 0.320 0.286

Correlation response model:

We wanted to data the relationship between the pairwise correlations and distance, size ratios, species-pairs, and locations of all of the trees. We built hierarchical mixed models with the pairwise correlations as a responses (normal truncated response (-1,1)).

##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: pearson_r | trunc(lb = -1.001, ub = 1.001) ~ dist + sizeratio + (1 | pair/Region:hilo) + (1 | Region:hilo/Neighborhood.x) 
##    Data: alldata (Number of observations: 918) 
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup samples = 4000
## 
## Group-Level Effects: 
## ~pair (Number of levels: 10) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.08      0.03     0.03     0.16 1.00     1578     2074
## 
## ~pair:Region:hilo (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.06      0.02     0.03     0.10 1.00     1282     2161
## 
## ~Region:hilo (Number of levels: 7) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.11      0.06     0.01     0.27 1.00      770      774
## 
## ~Region:hilo:Neighborhood.x (Number of levels: 21) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.11      0.03     0.07     0.17 1.00     1348     2365
## 
## Population-Level Effects: 
##           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept     0.33      0.06     0.21     0.45 1.00     2095     2304
## dist         -0.02      0.01    -0.04    -0.01 1.00     7052     3113
## sizeratio    -0.02      0.01    -0.03    -0.00 1.00     7702     2772
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.18      0.00     0.17     0.19 1.00     6828     2796
## 
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample 
## is a crude measure of effective sample size, and Rhat is the potential 
## scale reduction factor on split chains (at convergence, Rhat = 1).

Species pair intercepts
pair spp_mean .lower .upper .width
ac-ac 0.4299308 0.3125735 0.5504589 0.95
ac-pj 0.2895771 0.1742056 0.4112417 0.95
ac-pl 0.3347854 0.2199933 0.4538857 0.95
ac-pp 0.2608846 0.1022052 0.4055108 0.95
pj-pj 0.3029418 0.1848707 0.4216935 0.95
pj-pl 0.2968228 0.1804234 0.4173941 0.95
pj-pp 0.3483507 0.2020051 0.5036207 0.95
pl-pl 0.4172842 0.2942625 0.5467758 0.95
pl-pp 0.2979674 0.1473677 0.4423177 0.95
pp-pp 0.3071704 0.1441655 0.4588228 0.95
Conditional species pair estimates
pair .value .lower .upper .width
ac-ac 0.4387708 0.3226548 0.5563286 0.95
ac-pj 0.2990584 0.1841286 0.4216713 0.95
ac-pl 0.3443731 0.2280349 0.4630147 0.95
ac-pp 0.2702899 0.1119400 0.4161674 0.95
pj-pj 0.3128785 0.1941582 0.4305085 0.95
pj-pl 0.3063874 0.1897233 0.4256633 0.95
pj-pp 0.3576522 0.2112857 0.5111900 0.95
pl-pl 0.4263587 0.3045571 0.5526348 0.95
pl-pp 0.3071737 0.1561637 0.4512196 0.95
pp-pp 0.3168582 0.1515273 0.4684363 0.95

Site intercepts
Region hilo mean mean.lower mean.upper .width
Mammoth high 0.4261706 0.2779546 0.5845998 0.95
San.Jac high 0.3211825 0.1945011 0.4468180 0.95
San.Jac low 0.3735080 0.2482383 0.5118101 0.95
SEKI high 0.2309234 0.0798710 0.3788555 0.95
SEKI low 0.2679966 0.1321744 0.3985046 0.95
SENF high 0.3247677 0.1904712 0.4463505 0.95
SENF low 0.3533152 0.2198490 0.4840910 0.95
Conditional species pair estimates
Region hilo .value .lower .upper .width Site total_ppt_mm_fn1 mean_temp_C_fn1 spei12_fn1 total_ppt_mm_fn2 mean_temp_C_fn2 spei12_fn2 ppt_cv temp_cv pca1 pca2 site
Mammoth high 0.4361825 0.2864044 0.5895564 0.95 sl 662.8551 4.976681 0.0056064 243.8779 0.8644964 0.9924980 0.3679204 0.1737094 0.3994751 1.8371042 Mammoth_high
San.Jac high 0.3307396 0.2043351 0.4566170 0.95 bm 726.5933 8.650685 0.0067780 276.3013 0.8554435 0.9986706 0.3802695 0.0988874 -0.7095735 0.2417688 San.Jac_high
San.Jac low 0.3827795 0.2584360 0.5192507 0.95 sp 685.1577 11.096213 0.0069195 260.5055 0.8059019 0.9987380 0.3802125 0.0726285 -1.7676989 -0.5002259 San.Jac_low
SEKI high 0.2406349 0.0888628 0.3894296 0.95 pr 1113.5588 6.734041 0.0066853 397.6937 0.9431085 0.9933142 0.3571376 0.1400509 1.4720001 -0.5289892 SEKI_high
SEKI low 0.2776652 0.1420893 0.4083442 0.95 cm 1081.8940 8.423422 0.0062335 385.8646 0.9270428 0.9923128 0.3566565 0.1100554 0.7294427 -1.0299620 SEKI_low
SENF high 0.3345610 0.1997250 0.4558551 0.95 pp 896.6415 7.340703 0.0070685 325.4096 0.8139782 0.9953052 0.3629206 0.1108856 0.4212430 0.0752121 SENF_high
SENF low 0.3625846 0.2289590 0.4917346 0.95 lc 792.3074 8.884342 0.0067976 288.6899 0.8171269 0.9965620 0.3643661 0.0919738 -0.5448884 -0.0949081 SENF_low 
## 
## Call:
## lm(formula = data$mean ~ data$total_ppt_mm_fn1)
## 
## Residuals:
##         1         2         3         4         5         6         7 
##  0.037445 -0.047092 -0.008061 -0.013192  0.013722  0.011054  0.006125 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            6.014e-01  5.548e-02  10.840 0.000116 ***
## data$total_ppt_mm_fn1 -3.209e-04  6.388e-05  -5.022 0.004027 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02901 on 5 degrees of freedom
## Multiple R-squared:  0.8346, Adjusted R-squared:  0.8015 
## F-statistic: 25.22 on 1 and 5 DF,  p-value: 0.004027
## 
## Call:
## lm(formula = site_summ$.value ~ site_summ$total_ppt_mm_fn1)
## 
## Residuals:
##         1         2         3         4         5         6         7 
##  0.037896 -0.047113 -0.008357 -0.013163  0.013716  0.011223  0.005799 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 6.108e-01  5.574e-02  10.958  0.00011 ***
## site_summ$total_ppt_mm_fn1 -3.206e-04  6.419e-05  -4.995  0.00412 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02914 on 5 degrees of freedom
## Multiple R-squared:  0.833,  Adjusted R-squared:  0.7996 
## F-statistic: 24.95 on 1 and 5 DF,  p-value: 0.004124

## 
## Call:
## lm(formula = .value ~ total_ppt_mm_fn1 * pair, data = site_sp_summ)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.06631 -0.01452  0.00000  0.01797  0.07175 
## 
## Coefficients: (1 not defined because of singularities)
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 6.369e-01  7.817e-02   8.148 1.25e-08 ***
## total_ppt_mm_fn1           -2.201e-04  9.001e-05  -2.446 0.021544 *  
## pairac-pj                  -2.856e-01  1.175e-01  -2.431 0.022264 *  
## pairac-pl                  -2.268e-01  1.195e-01  -1.897 0.068934 .  
## pairac-pp                  -5.076e-01  1.533e-01  -3.310 0.002737 ** 
## pairpj-pj                  -3.663e-01  1.105e-01  -3.314 0.002712 ** 
## pairpj-pl                  -3.453e-01  1.195e-01  -2.888 0.007702 ** 
## pairpj-pp                  -2.880e-01  1.533e-01  -1.879 0.071568 .  
## pairpl-pl                  -2.163e-01  1.195e-01  -1.810 0.081885 .  
## pairpl-pp                  -3.976e-01  1.533e-01  -2.593 0.015420 *  
## pairpp-pp                  -1.876e-01  4.618e-02  -4.063 0.000397 ***
## total_ppt_mm_fn1:pairac-pj  1.540e-04  1.331e-04   1.158 0.257549    
## total_ppt_mm_fn1:pairac-pl  1.458e-04  1.351e-04   1.079 0.290339    
## total_ppt_mm_fn1:pairac-pp  3.511e-04  1.712e-04   2.050 0.050553 .  
## total_ppt_mm_fn1:pairpj-pj  2.652e-04  1.273e-04   2.083 0.047192 *  
## total_ppt_mm_fn1:pairpj-pl  2.304e-04  1.351e-04   1.706 0.099957 .  
## total_ppt_mm_fn1:pairpj-pp  2.380e-04  1.712e-04   1.390 0.176314    
## total_ppt_mm_fn1:pairpl-pl  2.403e-04  1.351e-04   1.779 0.086863 .  
## total_ppt_mm_fn1:pairpl-pp  2.846e-04  1.712e-04   1.662 0.108523    
## total_ppt_mm_fn1:pairpp-pp         NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04087 on 26 degrees of freedom
## Multiple R-squared:  0.8265, Adjusted R-squared:  0.7063 
## F-statistic: 6.879 on 18 and 26 DF,  p-value: 6.499e-06

Q3 Synchrony through time

Pairwise pearson correlations through time:

We calculated pearson correlations between pairs of individuals within neighborhoods for 30 year time blocks with a 10 year lag to measure synchrony through time. Trends were analyzed for data summarized for species-pairs at the neighborhood level. Note this is measuring within population synchrony (in contrast to Shestakova spatial synchrony).

Spline model:

I wanted to explore fitting a spline model to look at nonlinear changes in synchrony over time for different species-pairs and at different sites.

## pearson_r ~ s(decade)

## pearson_r ~ pair + s(decade, by = pair)

## pearson_r ~ Site.x + s(decade, by = Site.x)

Climate response model:

Model selection supported SPEI as the best predictor for synchrony. I included both mean and sd in one model although the variables are correlatedd (~.3). I did not do multiple regression because of multicollinearity.

## pearson_r | trunc(lb = -1.001, ub = 1.001) ~ total_ppt_mm_cv + (total_ppt_mm_cv | Site.x) + (1 | Site.x:pair)